Season the steaks generously with salt and pepper. In a large cast-iron skillet, melt 2 tablespoons of the butter. Add the steaks and cook over high heat, turning once, until medium-rare, 6 minutes total. Transfer to a carving board and let rest for 10 minutes.

Meanwhile, in a medium saucepan, melt 2 tablespoons of the butter in the olive oil. Add the shallots and cook over moderate heat, stirring occasionally, until softened and lightly browned, about 8 minutes. Add the red wine, vinegar and sugar and simmer until reduced by half, 3 to 5 minutes. Remove from the heat and whisk in the remaining 1 tablespoon of butter. Season the sauce with salt and pepper.